Divide the following complex numbers. $ \dfrac{-10-10i}{-5i}$
Explanation: Since we're dividing by a single term, we can simply divide each term in the numerator separately. $ \dfrac{-10-10i}{-5i} = \dfrac{-10}{-5i} - \dfrac{10i}{-5i}$ Factor out a $1/i$ $\dfrac{-10}{-5i} - \dfrac{10i}{-5i} = \dfrac 1i \left( \dfrac{-10}{-5} - \dfrac{10i}{-5} \right) = \dfrac 1i (2+2i)$ After simplification, $1/i$ is equal to $-i$, so we have: $\dfrac 1i (2+2i) = -i (2+2i) = -2i - 2i^2 = 2-2i$